Characterizing multiloop topologies is an important step towards developing novel methods at high perturbative orders in quantum field theory. In this article, we exploit the Loop-Tree Duality (LTD) formalism to analyse that appear for first time five loops. Explicitly, open loops into connected trees and group them according their topological properties. Then, identify a kernel generator, so-c...

OPTCON is an algorithm for the optimal control of nonlinear stochastic systems which particularly applicable to economic models. It delivers approximate numerical solutions optimum (dynamic optimization) problems with a quadratic objective function models additive and multiplicative (parameter) uncertainties. The was first programmed in C# then MATLAB. allows deterministic control, latter open ...

In this paper a new method is introduced and investigated for removing the destabilizing effects of time-delay parameter in control loops. The concept of the method is taken from the knowledge concerning the dynamic behaviour of irrational transfer functions (Ir-TF), which is discussed and investigated elswhere in frequency response domain and is explained briefly here. Ir-TFs, which are we...

We introduce a new technique to generate scattering amplitudes at one loop. Traditional tree algorithms, which handle diagrams with fixed momenta, are promoted to generators of loop-momentum polynomials that we call open loops. Combining open loops with tensor-integral and Ossola-Papadopoulos-Pittau reduction results in a fully flexible, very fast, and numerically stable one-loop generator. As ...